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Trend and Cycles: A New Approach and Explanations of Some Old Puzzles

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  • Tatsuma Wada
  • Pierre Perron

Abstract

Recent work on trend-cycle decompositions for US real GDP yields the following puzzling features: method based on Unobserved Components models, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bears little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycles, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of the presence of a change in the slope of the trend function in real GDP in 1973. Once this is properly accounted for, the results show all methods to yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. This cycle is more important in magnitude than previously reported, it accords very well with the NBER chronology and imply no correlation between the trend and cycle, since the former is non-stochastic. We propose a new approach to univariate trend-cycle decompositions using a generalized Unobserved Components models with errors having a mixture of Normals distribution for both the slope of the trend function and the cycle components. It can account endogenously for infrequent changes such as level shifts and change in slope, as well as different variances for expansions and recessions. It yields a decomposition that accords very well with common notions of the business cycles

Suggested Citation

  • Tatsuma Wada & Pierre Perron, 2005. "Trend and Cycles: A New Approach and Explanations of Some Old Puzzles," Computing in Economics and Finance 2005 252, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:252
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    1. Efectos no neutrales en los shocks monetarios
      by Nicolas Cachanosky in Punto de Vista Economico on 2013-11-15 09:01:59

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    Cited by:

    1. Arabinda Basistha, 2007. "Trend-cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP," Canadian Journal of Economics, Canadian Economics Association, vol. 40(2), pages 584-606, May.
    2. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    3. Ghent, Andra, 2006. "Comparing Models of Macroeconomic Fluctuations: How Big Are the Differences?," MPRA Paper 180, University Library of Munich, Germany.
    4. Arabinda Basistha, 2009. "Hours per capita and productivity: evidence from correlated unobserved components models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 187-206.
    5. B. Bhaskara Rao, 2010. "Deterministic and stochastic trends in the time series models: a guide for the applied economist," Applied Economics, Taylor & Francis Journals, vol. 42(17), pages 2193-2202.

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    More about this item

    Keywords

    Trend-Cycle Decomposition; Structural Change; Non Gaussian Filtering; Unobserved Components Model; Beveridge-Nelson Decomposition;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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